Write an expression for the model. Find the sum.
2 answers:
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Answer:
1) x = 15
Step-by-step explanation:
We use the Pythagorean thm for these questions. Where a and b are the legs (So order doesn't matter), and where c is the hypotenuse
1)
a² + b² = c²
9² + 12² = x²
81 + 144 = x²
x² = 225
You square root each side so you can get rid of the exponent on x.
x = 15
Answer: 3.217 & 12.434
Step-by-step explanation:
If we use <em>w</em> to represent the width, the length will be 6 more than 2 times w.
Hence, the length is .
The area of a rectangle would be its length times its width, so let's make an equation to represent it's area.
We can also substitute 40 in for A as it's given in the question.
Distributing <em>w</em> by multiplying it by both terms in the parentheses, we get
We can make the equation simpler by dividing both sides by 2.
Subtracting both sides by 20 will make the left-hand side 0.
Now that we have put this <em>quadratic equation</em> into standard form (ax²+bx+c), we can find its solutions using the quadratic formula.
For reference, the quadratic formula is
In this case, a is 1, b is 3, and c is -20.
Substituting, we get
Since the second solution results in a negative number, it cannot be the length of w.
The width/breadth of the rectangle is 3.217 cm.
To calculate the length, let's substitute the width into the expression for the length:
The length of this rectangle is 12.434 cm.